If one is given a differential equation, e. g. the KdV equation $\ u_t + u_{xxx} + uu_x = 0$, how can he find all of the symmetries of the differential equation? Is there also a method that works for integral equations?
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2 Answers
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A very nice survey is given by Francesco Oliveri.
Oliveri, Francesco, Lie symmetries of differential equations: classical results and recent contributions, Symmetry 2, No. 2, 658-706 (2010). ZBL1284.22014.
He has plenty of references, in particular to computer algebra system implementations of the algorithm (which goes back to Lie). See, e.g. reference 15.
See also this mathematica stackexchange question if you just care about the implementations.
answered Oct 1, 2017 at 15:07
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In fact, KdV has not just the Lie point symmetries discussed in the Oliveri paper from the answer of Igor Rivin but also infinitely many generalized (a.k.a. higher) symmetries, see e.g. Chapter 5 of the book Applications of Lie groups to differential equations by Peter Olver.
answered Aug 8, 2018 at 0:38
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$\begingroup$ Off-topic, but could you please slow down with your barrage of recent edits to questions (mainly adding tags) since this bumps questions to the front page and pushes other questions off the front page $\endgroup$ Commented Sep 9, 2018 at 15:11